What problem does this service solve?

Primecoin uses prime number generation to improve Bitcoin's PoW protocol.Ripple is an exchange and remittance network that aims to to allow fast financial transactions between banks, at minimal cost. Its protocol is built upon an open source distributed consensus ledger. XRP is the native currency that acts as a bridge currency between financial institutions to settle payments.

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Primecoin is a cryptocurrency based on finding prime numbers. Identifying prime numbers plays a central role in cryptography. Primecoin's unique Proof-of-Work (PoW) consensus mechanism is able to increase transaction speeds and improve energy efficiency.
The network searches for special prime number chains known as Cunningham chains and bi-twin chains, which are of interest in mathematical research.

Ripple is a real-time settlement and remittance network that is designed for the banking industry. Its settlement infrastructure technology has been adopted by a growing list of financial institutions looking to leverage the benefits of distributed ledgers. Ripple's real-time settlement network connects banks and enables cross border settlements and transactions in real-time. The current settlement infrastructure requires many intermediaries, and performing transactions take time and cost money. Ripple provides the underlying infrastructure for banks, and enables these transactions to be executed directly at almost no cost.

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